524 lines
18 KiB
Python
524 lines
18 KiB
Python
from sympy.core import (S, pi, oo, symbols, Function, Rational, Integer,
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Tuple, Symbol, EulerGamma, GoldenRatio, Catalan,
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Lambda, Mul, Pow, Mod, Eq, Ne, Le, Lt, Gt, Ge)
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from sympy.codegen.matrix_nodes import MatrixSolve
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from sympy.functions import (arg, atan2, bernoulli, beta, ceiling, chebyshevu,
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chebyshevt, conjugate, DiracDelta, exp, expint,
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factorial, floor, harmonic, Heaviside, im,
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laguerre, LambertW, log, Max, Min, Piecewise,
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polylog, re, RisingFactorial, sign, sinc, sqrt,
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zeta, binomial, legendre, dirichlet_eta,
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riemann_xi)
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from sympy.functions import (sin, cos, tan, cot, sec, csc, asin, acos, acot,
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atan, asec, acsc, sinh, cosh, tanh, coth, csch,
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sech, asinh, acosh, atanh, acoth, asech, acsch)
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from sympy.testing.pytest import raises, XFAIL
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from sympy.utilities.lambdify import implemented_function
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from sympy.matrices import (eye, Matrix, MatrixSymbol, Identity,
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HadamardProduct, SparseMatrix, HadamardPower)
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from sympy.functions.special.bessel import (jn, yn, besselj, bessely, besseli,
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besselk, hankel1, hankel2, airyai,
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airybi, airyaiprime, airybiprime)
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from sympy.functions.special.gamma_functions import (gamma, lowergamma,
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uppergamma, loggamma,
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polygamma)
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from sympy.functions.special.error_functions import (Chi, Ci, erf, erfc, erfi,
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erfcinv, erfinv, fresnelc,
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fresnels, li, Shi, Si, Li,
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erf2, Ei)
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from sympy.printing.octave import octave_code, octave_code as mcode
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x, y, z = symbols('x,y,z')
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def test_Integer():
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assert mcode(Integer(67)) == "67"
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assert mcode(Integer(-1)) == "-1"
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def test_Rational():
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assert mcode(Rational(3, 7)) == "3/7"
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assert mcode(Rational(18, 9)) == "2"
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assert mcode(Rational(3, -7)) == "-3/7"
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assert mcode(Rational(-3, -7)) == "3/7"
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assert mcode(x + Rational(3, 7)) == "x + 3/7"
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assert mcode(Rational(3, 7)*x) == "3*x/7"
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def test_Relational():
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assert mcode(Eq(x, y)) == "x == y"
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assert mcode(Ne(x, y)) == "x != y"
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assert mcode(Le(x, y)) == "x <= y"
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assert mcode(Lt(x, y)) == "x < y"
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assert mcode(Gt(x, y)) == "x > y"
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assert mcode(Ge(x, y)) == "x >= y"
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def test_Function():
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assert mcode(sin(x) ** cos(x)) == "sin(x).^cos(x)"
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assert mcode(sign(x)) == "sign(x)"
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assert mcode(exp(x)) == "exp(x)"
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assert mcode(log(x)) == "log(x)"
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assert mcode(factorial(x)) == "factorial(x)"
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assert mcode(floor(x)) == "floor(x)"
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assert mcode(atan2(y, x)) == "atan2(y, x)"
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assert mcode(beta(x, y)) == 'beta(x, y)'
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assert mcode(polylog(x, y)) == 'polylog(x, y)'
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assert mcode(harmonic(x)) == 'harmonic(x)'
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assert mcode(bernoulli(x)) == "bernoulli(x)"
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assert mcode(bernoulli(x, y)) == "bernoulli(x, y)"
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assert mcode(legendre(x, y)) == "legendre(x, y)"
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def test_Function_change_name():
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assert mcode(abs(x)) == "abs(x)"
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assert mcode(ceiling(x)) == "ceil(x)"
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assert mcode(arg(x)) == "angle(x)"
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assert mcode(im(x)) == "imag(x)"
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assert mcode(re(x)) == "real(x)"
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assert mcode(conjugate(x)) == "conj(x)"
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assert mcode(chebyshevt(y, x)) == "chebyshevT(y, x)"
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assert mcode(chebyshevu(y, x)) == "chebyshevU(y, x)"
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assert mcode(laguerre(x, y)) == "laguerreL(x, y)"
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assert mcode(Chi(x)) == "coshint(x)"
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assert mcode(Shi(x)) == "sinhint(x)"
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assert mcode(Ci(x)) == "cosint(x)"
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assert mcode(Si(x)) == "sinint(x)"
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assert mcode(li(x)) == "logint(x)"
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assert mcode(loggamma(x)) == "gammaln(x)"
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assert mcode(polygamma(x, y)) == "psi(x, y)"
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assert mcode(RisingFactorial(x, y)) == "pochhammer(x, y)"
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assert mcode(DiracDelta(x)) == "dirac(x)"
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assert mcode(DiracDelta(x, 3)) == "dirac(3, x)"
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assert mcode(Heaviside(x)) == "heaviside(x, 1/2)"
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assert mcode(Heaviside(x, y)) == "heaviside(x, y)"
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assert mcode(binomial(x, y)) == "bincoeff(x, y)"
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assert mcode(Mod(x, y)) == "mod(x, y)"
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def test_minmax():
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assert mcode(Max(x, y) + Min(x, y)) == "max(x, y) + min(x, y)"
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assert mcode(Max(x, y, z)) == "max(x, max(y, z))"
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assert mcode(Min(x, y, z)) == "min(x, min(y, z))"
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def test_Pow():
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assert mcode(x**3) == "x.^3"
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assert mcode(x**(y**3)) == "x.^(y.^3)"
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assert mcode(x**Rational(2, 3)) == 'x.^(2/3)'
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g = implemented_function('g', Lambda(x, 2*x))
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assert mcode(1/(g(x)*3.5)**(x - y**x)/(x**2 + y)) == \
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"(3.5*2*x).^(-x + y.^x)./(x.^2 + y)"
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# For issue 14160
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assert mcode(Mul(-2, x, Pow(Mul(y,y,evaluate=False), -1, evaluate=False),
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evaluate=False)) == '-2*x./(y.*y)'
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def test_basic_ops():
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assert mcode(x*y) == "x.*y"
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assert mcode(x + y) == "x + y"
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assert mcode(x - y) == "x - y"
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assert mcode(-x) == "-x"
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def test_1_over_x_and_sqrt():
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# 1.0 and 0.5 would do something different in regular StrPrinter,
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# but these are exact in IEEE floating point so no different here.
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assert mcode(1/x) == '1./x'
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assert mcode(x**-1) == mcode(x**-1.0) == '1./x'
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assert mcode(1/sqrt(x)) == '1./sqrt(x)'
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assert mcode(x**-S.Half) == mcode(x**-0.5) == '1./sqrt(x)'
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assert mcode(sqrt(x)) == 'sqrt(x)'
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assert mcode(x**S.Half) == mcode(x**0.5) == 'sqrt(x)'
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assert mcode(1/pi) == '1/pi'
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assert mcode(pi**-1) == mcode(pi**-1.0) == '1/pi'
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assert mcode(pi**-0.5) == '1/sqrt(pi)'
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def test_mix_number_mult_symbols():
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assert mcode(3*x) == "3*x"
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assert mcode(pi*x) == "pi*x"
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assert mcode(3/x) == "3./x"
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assert mcode(pi/x) == "pi./x"
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assert mcode(x/3) == "x/3"
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assert mcode(x/pi) == "x/pi"
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assert mcode(x*y) == "x.*y"
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assert mcode(3*x*y) == "3*x.*y"
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assert mcode(3*pi*x*y) == "3*pi*x.*y"
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assert mcode(x/y) == "x./y"
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assert mcode(3*x/y) == "3*x./y"
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assert mcode(x*y/z) == "x.*y./z"
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assert mcode(x/y*z) == "x.*z./y"
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assert mcode(1/x/y) == "1./(x.*y)"
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assert mcode(2*pi*x/y/z) == "2*pi*x./(y.*z)"
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assert mcode(3*pi/x) == "3*pi./x"
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assert mcode(S(3)/5) == "3/5"
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assert mcode(S(3)/5*x) == "3*x/5"
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assert mcode(x/y/z) == "x./(y.*z)"
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assert mcode((x+y)/z) == "(x + y)./z"
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assert mcode((x+y)/(z+x)) == "(x + y)./(x + z)"
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assert mcode((x+y)/EulerGamma) == "(x + y)/%s" % EulerGamma.evalf(17)
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assert mcode(x/3/pi) == "x/(3*pi)"
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assert mcode(S(3)/5*x*y/pi) == "3*x.*y/(5*pi)"
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def test_mix_number_pow_symbols():
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assert mcode(pi**3) == 'pi^3'
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assert mcode(x**2) == 'x.^2'
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assert mcode(x**(pi**3)) == 'x.^(pi^3)'
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assert mcode(x**y) == 'x.^y'
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assert mcode(x**(y**z)) == 'x.^(y.^z)'
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assert mcode((x**y)**z) == '(x.^y).^z'
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def test_imag():
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I = S('I')
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assert mcode(I) == "1i"
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assert mcode(5*I) == "5i"
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assert mcode((S(3)/2)*I) == "3*1i/2"
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assert mcode(3+4*I) == "3 + 4i"
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assert mcode(sqrt(3)*I) == "sqrt(3)*1i"
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def test_constants():
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assert mcode(pi) == "pi"
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assert mcode(oo) == "inf"
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assert mcode(-oo) == "-inf"
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assert mcode(S.NegativeInfinity) == "-inf"
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assert mcode(S.NaN) == "NaN"
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assert mcode(S.Exp1) == "exp(1)"
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assert mcode(exp(1)) == "exp(1)"
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def test_constants_other():
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assert mcode(2*GoldenRatio) == "2*(1+sqrt(5))/2"
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assert mcode(2*Catalan) == "2*%s" % Catalan.evalf(17)
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assert mcode(2*EulerGamma) == "2*%s" % EulerGamma.evalf(17)
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def test_boolean():
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assert mcode(x & y) == "x & y"
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assert mcode(x | y) == "x | y"
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assert mcode(~x) == "~x"
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assert mcode(x & y & z) == "x & y & z"
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assert mcode(x | y | z) == "x | y | z"
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assert mcode((x & y) | z) == "z | x & y"
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assert mcode((x | y) & z) == "z & (x | y)"
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def test_KroneckerDelta():
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from sympy.functions import KroneckerDelta
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assert mcode(KroneckerDelta(x, y)) == "double(x == y)"
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assert mcode(KroneckerDelta(x, y + 1)) == "double(x == (y + 1))"
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assert mcode(KroneckerDelta(2**x, y)) == "double((2.^x) == y)"
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def test_Matrices():
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assert mcode(Matrix(1, 1, [10])) == "10"
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A = Matrix([[1, sin(x/2), abs(x)],
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[0, 1, pi],
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[0, exp(1), ceiling(x)]]);
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expected = "[1 sin(x/2) abs(x); 0 1 pi; 0 exp(1) ceil(x)]"
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assert mcode(A) == expected
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# row and columns
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assert mcode(A[:,0]) == "[1; 0; 0]"
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assert mcode(A[0,:]) == "[1 sin(x/2) abs(x)]"
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# empty matrices
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assert mcode(Matrix(0, 0, [])) == '[]'
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assert mcode(Matrix(0, 3, [])) == 'zeros(0, 3)'
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# annoying to read but correct
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assert mcode(Matrix([[x, x - y, -y]])) == "[x x - y -y]"
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def test_vector_entries_hadamard():
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# For a row or column, user might to use the other dimension
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A = Matrix([[1, sin(2/x), 3*pi/x/5]])
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assert mcode(A) == "[1 sin(2./x) 3*pi./(5*x)]"
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assert mcode(A.T) == "[1; sin(2./x); 3*pi./(5*x)]"
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@XFAIL
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def test_Matrices_entries_not_hadamard():
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# For Matrix with col >= 2, row >= 2, they need to be scalars
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# FIXME: is it worth worrying about this? Its not wrong, just
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# leave it user's responsibility to put scalar data for x.
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A = Matrix([[1, sin(2/x), 3*pi/x/5], [1, 2, x*y]])
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expected = ("[1 sin(2/x) 3*pi/(5*x);\n"
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"1 2 x*y]") # <- we give x.*y
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assert mcode(A) == expected
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def test_MatrixSymbol():
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n = Symbol('n', integer=True)
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A = MatrixSymbol('A', n, n)
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B = MatrixSymbol('B', n, n)
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assert mcode(A*B) == "A*B"
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assert mcode(B*A) == "B*A"
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assert mcode(2*A*B) == "2*A*B"
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assert mcode(B*2*A) == "2*B*A"
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assert mcode(A*(B + 3*Identity(n))) == "A*(3*eye(n) + B)"
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assert mcode(A**(x**2)) == "A^(x.^2)"
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assert mcode(A**3) == "A^3"
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assert mcode(A**S.Half) == "A^(1/2)"
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def test_MatrixSolve():
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n = Symbol('n', integer=True)
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A = MatrixSymbol('A', n, n)
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x = MatrixSymbol('x', n, 1)
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assert mcode(MatrixSolve(A, x)) == "A \\ x"
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def test_special_matrices():
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assert mcode(6*Identity(3)) == "6*eye(3)"
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def test_containers():
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assert mcode([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \
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"{1, 2, 3, {4, 5, {6, 7}}, 8, {9, 10}, 11}"
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assert mcode((1, 2, (3, 4))) == "{1, 2, {3, 4}}"
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assert mcode([1]) == "{1}"
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assert mcode((1,)) == "{1}"
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assert mcode(Tuple(*[1, 2, 3])) == "{1, 2, 3}"
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assert mcode((1, x*y, (3, x**2))) == "{1, x.*y, {3, x.^2}}"
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# scalar, matrix, empty matrix and empty list
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assert mcode((1, eye(3), Matrix(0, 0, []), [])) == "{1, [1 0 0; 0 1 0; 0 0 1], [], {}}"
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def test_octave_noninline():
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source = mcode((x+y)/Catalan, assign_to='me', inline=False)
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expected = (
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"Catalan = %s;\n"
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"me = (x + y)/Catalan;"
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) % Catalan.evalf(17)
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assert source == expected
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def test_octave_piecewise():
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expr = Piecewise((x, x < 1), (x**2, True))
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assert mcode(expr) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))"
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assert mcode(expr, assign_to="r") == (
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"r = ((x < 1).*(x) + (~(x < 1)).*(x.^2));")
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assert mcode(expr, assign_to="r", inline=False) == (
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"if (x < 1)\n"
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" r = x;\n"
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"else\n"
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" r = x.^2;\n"
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"end")
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expr = Piecewise((x**2, x < 1), (x**3, x < 2), (x**4, x < 3), (x**5, True))
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expected = ("((x < 1).*(x.^2) + (~(x < 1)).*( ...\n"
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"(x < 2).*(x.^3) + (~(x < 2)).*( ...\n"
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"(x < 3).*(x.^4) + (~(x < 3)).*(x.^5))))")
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assert mcode(expr) == expected
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assert mcode(expr, assign_to="r") == "r = " + expected + ";"
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assert mcode(expr, assign_to="r", inline=False) == (
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"if (x < 1)\n"
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" r = x.^2;\n"
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"elseif (x < 2)\n"
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" r = x.^3;\n"
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"elseif (x < 3)\n"
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" r = x.^4;\n"
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"else\n"
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" r = x.^5;\n"
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"end")
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# Check that Piecewise without a True (default) condition error
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expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
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raises(ValueError, lambda: mcode(expr))
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def test_octave_piecewise_times_const():
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pw = Piecewise((x, x < 1), (x**2, True))
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assert mcode(2*pw) == "2*((x < 1).*(x) + (~(x < 1)).*(x.^2))"
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assert mcode(pw/x) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))./x"
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assert mcode(pw/(x*y)) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))./(x.*y)"
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assert mcode(pw/3) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))/3"
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def test_octave_matrix_assign_to():
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A = Matrix([[1, 2, 3]])
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assert mcode(A, assign_to='a') == "a = [1 2 3];"
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A = Matrix([[1, 2], [3, 4]])
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assert mcode(A, assign_to='A') == "A = [1 2; 3 4];"
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def test_octave_matrix_assign_to_more():
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# assigning to Symbol or MatrixSymbol requires lhs/rhs match
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A = Matrix([[1, 2, 3]])
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B = MatrixSymbol('B', 1, 3)
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C = MatrixSymbol('C', 2, 3)
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assert mcode(A, assign_to=B) == "B = [1 2 3];"
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raises(ValueError, lambda: mcode(A, assign_to=x))
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raises(ValueError, lambda: mcode(A, assign_to=C))
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def test_octave_matrix_1x1():
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A = Matrix([[3]])
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B = MatrixSymbol('B', 1, 1)
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C = MatrixSymbol('C', 1, 2)
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assert mcode(A, assign_to=B) == "B = 3;"
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# FIXME?
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#assert mcode(A, assign_to=x) == "x = 3;"
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raises(ValueError, lambda: mcode(A, assign_to=C))
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def test_octave_matrix_elements():
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A = Matrix([[x, 2, x*y]])
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assert mcode(A[0, 0]**2 + A[0, 1] + A[0, 2]) == "x.^2 + x.*y + 2"
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A = MatrixSymbol('AA', 1, 3)
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assert mcode(A) == "AA"
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assert mcode(A[0, 0]**2 + sin(A[0,1]) + A[0,2]) == \
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"sin(AA(1, 2)) + AA(1, 1).^2 + AA(1, 3)"
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assert mcode(sum(A)) == "AA(1, 1) + AA(1, 2) + AA(1, 3)"
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def test_octave_boolean():
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assert mcode(True) == "true"
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assert mcode(S.true) == "true"
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assert mcode(False) == "false"
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assert mcode(S.false) == "false"
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def test_octave_not_supported():
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assert mcode(S.ComplexInfinity) == (
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"% Not supported in Octave:\n"
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"% ComplexInfinity\n"
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"zoo"
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)
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f = Function('f')
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assert mcode(f(x).diff(x)) == (
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|
"% Not supported in Octave:\n"
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|
"% Derivative\n"
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|
"Derivative(f(x), x)"
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|
)
|
|
|
|
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def test_octave_not_supported_not_on_whitelist():
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from sympy.functions.special.polynomials import assoc_laguerre
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assert mcode(assoc_laguerre(x, y, z)) == (
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|
"% Not supported in Octave:\n"
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|
"% assoc_laguerre\n"
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|
"assoc_laguerre(x, y, z)"
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|
)
|
|
|
|
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def test_octave_expint():
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assert mcode(expint(1, x)) == "expint(x)"
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|
assert mcode(expint(2, x)) == (
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|
"% Not supported in Octave:\n"
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|
"% expint\n"
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|
"expint(2, x)"
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|
)
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|
assert mcode(expint(y, x)) == (
|
|
"% Not supported in Octave:\n"
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|
"% expint\n"
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|
"expint(y, x)"
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|
)
|
|
|
|
|
|
def test_trick_indent_with_end_else_words():
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|
# words starting with "end" or "else" do not confuse the indenter
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|
t1 = S('endless');
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|
t2 = S('elsewhere');
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pw = Piecewise((t1, x < 0), (t2, x <= 1), (1, True))
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assert mcode(pw, inline=False) == (
|
|
"if (x < 0)\n"
|
|
" endless\n"
|
|
"elseif (x <= 1)\n"
|
|
" elsewhere\n"
|
|
"else\n"
|
|
" 1\n"
|
|
"end")
|
|
|
|
|
|
def test_hadamard():
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|
A = MatrixSymbol('A', 3, 3)
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|
B = MatrixSymbol('B', 3, 3)
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|
v = MatrixSymbol('v', 3, 1)
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|
h = MatrixSymbol('h', 1, 3)
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|
C = HadamardProduct(A, B)
|
|
n = Symbol('n')
|
|
assert mcode(C) == "A.*B"
|
|
assert mcode(C*v) == "(A.*B)*v"
|
|
assert mcode(h*C*v) == "h*(A.*B)*v"
|
|
assert mcode(C*A) == "(A.*B)*A"
|
|
# mixing Hadamard and scalar strange b/c we vectorize scalars
|
|
assert mcode(C*x*y) == "(x.*y)*(A.*B)"
|
|
|
|
# Testing HadamardPower:
|
|
assert mcode(HadamardPower(A, n)) == "A.**n"
|
|
assert mcode(HadamardPower(A, 1+n)) == "A.**(n + 1)"
|
|
assert mcode(HadamardPower(A*B.T, 1+n)) == "(A*B.T).**(n + 1)"
|
|
|
|
|
|
def test_sparse():
|
|
M = SparseMatrix(5, 6, {})
|
|
M[2, 2] = 10;
|
|
M[1, 2] = 20;
|
|
M[1, 3] = 22;
|
|
M[0, 3] = 30;
|
|
M[3, 0] = x*y;
|
|
assert mcode(M) == (
|
|
"sparse([4 2 3 1 2], [1 3 3 4 4], [x.*y 20 10 30 22], 5, 6)"
|
|
)
|
|
|
|
|
|
def test_sinc():
|
|
assert mcode(sinc(x)) == 'sinc(x/pi)'
|
|
assert mcode(sinc(x + 3)) == 'sinc((x + 3)/pi)'
|
|
assert mcode(sinc(pi*(x + 3))) == 'sinc(x + 3)'
|
|
|
|
|
|
def test_trigfun():
|
|
for f in (sin, cos, tan, cot, sec, csc, asin, acos, acot, atan, asec, acsc,
|
|
sinh, cosh, tanh, coth, csch, sech, asinh, acosh, atanh, acoth,
|
|
asech, acsch):
|
|
assert octave_code(f(x) == f.__name__ + '(x)')
|
|
|
|
|
|
def test_specfun():
|
|
n = Symbol('n')
|
|
for f in [besselj, bessely, besseli, besselk]:
|
|
assert octave_code(f(n, x)) == f.__name__ + '(n, x)'
|
|
for f in (erfc, erfi, erf, erfinv, erfcinv, fresnelc, fresnels, gamma):
|
|
assert octave_code(f(x)) == f.__name__ + '(x)'
|
|
assert octave_code(hankel1(n, x)) == 'besselh(n, 1, x)'
|
|
assert octave_code(hankel2(n, x)) == 'besselh(n, 2, x)'
|
|
assert octave_code(airyai(x)) == 'airy(0, x)'
|
|
assert octave_code(airyaiprime(x)) == 'airy(1, x)'
|
|
assert octave_code(airybi(x)) == 'airy(2, x)'
|
|
assert octave_code(airybiprime(x)) == 'airy(3, x)'
|
|
assert octave_code(uppergamma(n, x)) == '(gammainc(x, n, \'upper\').*gamma(n))'
|
|
assert octave_code(lowergamma(n, x)) == '(gammainc(x, n).*gamma(n))'
|
|
assert octave_code(z**lowergamma(n, x)) == 'z.^(gammainc(x, n).*gamma(n))'
|
|
assert octave_code(jn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
|
|
assert octave_code(yn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
|
|
assert octave_code(LambertW(x)) == 'lambertw(x)'
|
|
assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'
|
|
|
|
# Automatic rewrite
|
|
assert octave_code(Ei(x)) == 'logint(exp(x))'
|
|
assert octave_code(dirichlet_eta(x)) == '((x == 1).*(log(2)) + (~(x == 1)).*((1 - 2.^(1 - x)).*zeta(x)))'
|
|
assert octave_code(riemann_xi(x)) == 'pi.^(-x/2).*x.*(x - 1).*gamma(x/2).*zeta(x)/2'
|
|
|
|
|
|
def test_MatrixElement_printing():
|
|
# test cases for issue #11821
|
|
A = MatrixSymbol("A", 1, 3)
|
|
B = MatrixSymbol("B", 1, 3)
|
|
C = MatrixSymbol("C", 1, 3)
|
|
|
|
assert mcode(A[0, 0]) == "A(1, 1)"
|
|
assert mcode(3 * A[0, 0]) == "3*A(1, 1)"
|
|
|
|
F = C[0, 0].subs(C, A - B)
|
|
assert mcode(F) == "(A - B)(1, 1)"
|
|
|
|
|
|
def test_zeta_printing_issue_14820():
|
|
assert octave_code(zeta(x)) == 'zeta(x)'
|
|
assert octave_code(zeta(x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
|
|
|
|
|
|
def test_automatic_rewrite():
|
|
assert octave_code(Li(x)) == 'logint(x) - logint(2)'
|
|
assert octave_code(erf2(x, y)) == '-erf(x) + erf(y)'
|